Sserdna:What if the officer has no proof?
The officer has proof. Proof is simply admissible evidence that supports the claim being made. His testimony as to what he observed of your driving is admissible evidence and, if the actions he describes would be careless driving, would be proof that you drove carelessly.
Sserdna:I thought I was innocent until proven guilty?
The presumption of innocence applies at the trial. What that presumption means is that the state bears the burden of proving its case at trial that you committed the charged offense. You don't have to prove innocence. If the case simply is the cop's testimony vs. your testimony, then the issue will be what version of events does the court believe. Quite often, it will be the cop's testimony that will be believed unless you can cast doubt on his testimony. Your own testimony is weakened by the simple fact that you are the one charged with a crime and thus your testimony is self-serving; i.e. you are trying to get acquitted, and might therefore provide a more favorable version of events than what really happened.
Sserdna:The only way he can prove that he saw what he saw (which I don't think he saw because I don't remember doing what he claims I did even seconds after he claims I did it) is if he had a camera on his car.
He doesn't need a camera showing what you did. Forget what you see on TV and movies. The state does not need scientific evidence, video or audio recordings, etc., to convict you. Testimony of eye witnesses is good evidence, and that alone can be enough to get you convicted. Here, the cop is the eye witness.
Sserdna:I don't know if he actually does have a camera on his car, but I heard that it is only on when his lights are on, which would definitely show me doing nothing.
That sounds kind of silly when you think about it, doesn't it? Why would the camera only work AFTER the flashing lights are turned on? Doing that would mean that cops lose the chance to catch video of the offense; they'd only ever record the events of the stop after the offense was committed. No police department I know of limits use of the cameras in that fashion.
You can ask the state for discovery to see what it intends to use against you at trial. Then you'll know if there is a video and get a copy of whatever video does exist.
Testifying as to how smart you are is not a good idea for the reasons Gemini mentioned. It would also be inadmissible since (1) you cannot testify to that yourself since it requires an expert witness to establish how you tested and what that means and (2) how smart you are is completely irrelevant to the issue before the court: did you drive carelessly? How smart you are doesn't do anything to shed light on that issue.
Having firefighter friends come in and testify how well you usually drive also is not admissible because it is not relevant. How well you drove on other occasions does not shed any light on how you drove on this particular occasion. The only witnesses that are worth bringing in on a matter like this are those who observed your driving at the time in question.
What you need to realize is that all the court will care about is evidence concerning how you were driving at the particular time in question. That's it. Anything that does not shed light on the issue of whether you were driving carelessly at that particular time is worthless. This means you either need to cast doubt on the accuracy of the state's evidence or submit rebuttal evidence of your own as to how you were driving at the time in question. In a case like this, that usually means trying attack the cop's testimony to show that he couldn't see things well or that he didn't remember things well, coupled with your testimony as to how you were driving. If the cop is experienced in testifying in court, it will likely be hard to show weakness in his testimony. That's the situation you are up against.
I recommend you see an attorney for help if you want the best possible outcome from this.